We discuss applications of wavelet transforms in signal processing. First we consider techniques for adapted data compression, especially for medical images, to describe a given image in a compact way. A similar task has to be managed in the area of feature extraction which is based on signal preprocessing methods. In this context we describe an alternative, optical realization of wavelets using diffractive elements (DE). The design of DEs is an inverse and ill-posed problem and we describe how approximated solutions are computed by a modified, iterative projection algorithm
